A spectrogram for the twenty-first century.


A spectrogram for the twenty-first century.







Noise, Echoes,

and more

A publication of

the Acoustical Society

of America

Report of the Vision 2010 Committee


Sean A. Fulop

Department of Linguistics, California State University, Fresno

Fresno, California 93740

Kelly Fitz

School of Electrical Engineering and Computer Science, Washington State University

Pullman, Washington 99164

Just as World War II was breaking

out in Europe in 1939, a prototype

of a remarkable electrical device

was being completed at Bell Telephone

Laboratories, under the direction of

Ralph Potter. This device was able to

provide, on a strip of paper, a continuous

running document of the Fourier

spectrum of a sound signal as it

changed through time. Because of the

war it was kept under wraps, but its

detailed construction and numerous

applications were revealed to the scientific

community in a series of papers

published in the Journal of the

Acoustical Society of America (JASA) in

1946, 1,2 wherein it was called the

Sound Spectrograph. The running

spectral analysis that it output was

termed a spectrogram.

The spectrograph has been recorded

in history as one of the most useful

and influential instruments for acoustic

signal processing. In particular, the

fields of phonetics and speech communication,

which motivated the development

of the machine, have been completely

transformed by its widespread

adoption. Over the decades, the cumbersome

and delicate analog spectrograph

hardware was transformed into

more robust digital hardware at first,

and then as computers became generally

more powerful, into the digital software

incarnations most of us use today.

The underlying principle of the spectrogram

has never changed; most applied

acousticians who do time-frequency

analysis are content to use software that

in essence simulates the output that

appeared 60 years ago in JASA (Fig. 1).

Of what else in acoustics can the same

be said? Do we use 60-year old microphones?

Tape recorders? Loudspeakers?

Well, in truth, some of us have not

been so content, but a more useful analytical

process has never been generally

recognized. The rich area of signal pro-

Fig. 1. Compare spectrograms of utterances [baeb], [daed], [gag] from a 1946 JASA paper 2 (upper panel) to ones

made in 2006 from the first author’s similar utterances, using the popular Praat sound analysis software.

cessing research known as “time-frequency

analysis” grew up during the

past 60 years. But the numerous variations

on the spectrogram that have been

touted (one can think of the Wigner-

Ville transform, or wavelet analysis)

have never made much impact in many

applied circles because of physical interpretation

problems, readability problems,

or simply because they were not

that much better. Time-frequency representations

other than the spectrogram,

while they may be more precise

for certain test signals like a pure chirp

(frequency-modulated sinusoid), usually

provide unwanted “cross-terms” that

do not correspond to physically or auditorily

interpretable sound (signal) components.

Ones that do not have this

problem do not look much better than a

spectrogram in any case. Wavelet processing

is better thought of as “timescale”

rather than “time-frequency,” and

yields representations which are hard to

read and interpret in spectrographic


In fact, one especially useful

improvement on the spectrogram (for

many applied purposes, at least) was

devised and implemented as software

thirty years ago, but it was somehow

drowned in the signal processing hubbub.

Too many hopeful but ultimately

useless efforts at time-frequency analysis

left everybody jaded and defeatist,

and it has taken these thirty years for

the interest, invention, and mathematical

analysis of a number of researchers

to bring us to a point where we can well

and truly say that there is something

out there which is better than a spectrogram.

The reassigned spectrogram is

ready for its close-up.

Fourier’s timeless problem

The time-frequency analysis of a

signal refers generally to a threedimensional

representation showing

the passage of time on one axis, the

range of frequencies on a second axis,

and the amplitude found in each timefrequency

intersection (or cell in the

digital domain) on a third axis. The

amplitude axis is traditionally shown

by linking the values to a grayscale colormap

over a two-dimensional timefrequency

matrix. This kind of timefrequency

representation attempts to

show the distribution of signal energy

over the time-frequency plane. The

archetypal time-frequency representation

is the spectrogram, which was

originally developed using analog electrical

filters, but which was eventually

26 Acoustics Today, July 2006

epresented mathematically as the magnitude of the shorttime

Fourier transform, 3 a two-dimensional time-varying

generalization of the Fourier transform.

Briefly put, for each time step of a signal, a spectrogram

(Fig. 2) shows the decomposition of an analysis window into

its Fourier spectral components as defined using the conventional

Fourier transform.

This analysis produces a problem resulting from the

inappropriateness of the Fourier transform’s formalization of

the colloquial notion of “frequency” when a short analysis

span is used in the spectrogram. A mathematical frequency

defined using the Fourier transform does not correspond to

our intuitive understanding of “frequency” unless the analysis

span is infinite in time, and this negates the ability of a

time-varying generalization of the scheme to tell us what we

want to know about each short frame. For example, the

Fourier spectrum of frequencies in a sine wave of infinite

extent is indeed just the frequency of the sine wave which we

would intuitively want (meaning, it is just exactly the backand-forth

rate of the oscillation), but when the sine wave is

not infinite-time, the Fourier spectrum instead yields a band

Fig. 2. Conventional (upper) and reassigned spectrograms of a pure double chirp

signal, both computed using 15.6 ms frames, 156 µsec frame overlap. The reassigned

spectrogram displays amplitudes from red (loud) to blue (quiet) in spectral

order. The increased precision of frequency tracking, is notable, in spite of visible

computational artifacts and interference lines.

Fig. 3. Fourier spectrum (green line) versus reassigned instantaneous frequency

spectrum (blue points) of a two-component signal, both computed from a single

Fourier transform over a 125 ms frame. The precise location of the 50 and 150 Hz

sinusoidal components is shown by computing their instantaneous frequencies and

reassigning points, but not by means of the Fourier frequency definition.

of frequencies surrounding and obscuring the intuitive frequency

of the sine wave (see Fig. 3).

This so-called “smearing” in frequency affects the conventional

spectrogram of Fig. 2, which is comprised of a sequence

of Fourier spectra of successive short analysis windows of the

signal. A mathematical duality within the transform induces a

corresponding smearing in time, which may serve to obscure

the true times of excitation of the various frequencies.

It is important to recognize that the frequency smearing

that is so egregious in a short frame spectrogram is not a

result of the uncertainty principle (shown by Denis Gabor 4 to

be analogous to the Heisenberg principle) which governs the

duality between time and frequency, as this affects the resolving

power of the transform in the time and frequency dimensions.

The smearing is a precision problem rather than a resolution

problem, and this is clear from the fact that even one

purely sinusoidal signal component will be smeared in a conventional

wideband spectrogram, whether or not we attempt

to resolve it from anything else.

In speech analysis and many other applications, the

investigator is frequently not interested in the time-frequency

energy distribution that the spectrogram provides, but is

rather more interested in the instantaneous frequencies of the

various amplitude-modulated (AM) or frequency-modulated

(FM) sinusoidal components (often called line components)

of a multicomponent signal. The instantaneous frequency 5,6 is

a suitable generalization of mathematical frequency that may

change over time. Specifically, it is defined as the derivative of

the frequency modulation function of a single line component—this

degenerates formally to the intuitive frequency of

an unmodulated sine wave, no matter how long or short that

sine wave is.

The reason to switch our mathematical model of intuitive

“frequency” from Fourier’s definition to that of instantaneous

frequency is chiefly this: It seems increasingly likely

that the human auditory system somehow pays attention

to instantaneous frequency rather than the classical Fourier

frequency. First, no one has reported that the auditory per-

A Spectrogram for the Twenty-First Century 27

ception of the spectral timbre of a single

unmodulated component (sine wave) is

different depending on how long the signal

was played, so long as the length of

time exceeds a minimum auditory threshold

of timbre perception. Additionally,

the human auditory system has the ability

to track the changing pitch of a frequency

modulated sinusoid over time, while

retaining the perception of sine wave timbre

just as if there were no frequency

modulation. Neither of these attributes is

true of the classical Fourier spectrum of

such sounds—a short sine wave supposedly

has a larger and louder band of extra

frequency components than a longer one,

and a chirp has a similar band of such

“components” surrounding the single modulated one we

know is there. So, the timbre analysis that is performed by

the ear and brain is probably not like a Fourier analysis,

since we do not auditorily experience the spectral smearing

of frequencies when they are modulated.

Components, by any other frame, would sound


The conventional spectrogram, as with all so-called

time-frequency representations, provides us with a picture of

how the signal’s energy is distributed in time and frequency—Fourier’s

frequency, that is. This is the root of its problems.

Rather than trying to improve this representation,

which decades of signal processing research have shown to

be impossible to any significant extent, a few independent

thinkers worked to develop a new kind of image that would

show the time course of the instantaneous frequencies of

the components in a multicomponent signal. The seminal

papers which put forth the original technique—called the

modified moving window method—were written by

Kunihiko Kodera and his colleagues C. de Villedary and R.

Gendrin. 7,8 Their jumping off point was a paper published

by Rihaczek 9 which demonstrated the connection between

instantaneous frequency and the argument (phase) of a

complex analytic signal—basically a complex version of a

real signal, where the nonphysical imaginary part is related

by the Hilbert transform to the physical real part. The main

insight added by Kodera et al. was the recognition that the

short-time Fourier transform—a 2D function having complex

values whose magnitude yields the spectrogram—can

be regarded as a “channelizing” of the signal into a bunch of

complex analytic signals, one for each Fourier spectral frequency,

from which the instantaneous frequencies of line

components in the signal can be computed.

Unfortunately their method was almost perfectly

ignored by the signal processing and acoustics communities

at that time and for many years afterward, an all-too-common

attribute of truly original work. More recently, however,

the idea has been revived through alternative methods,

10,11 and also followed up with theoretical improvements,

12 and these developments have led to the adoption of

the reassigned (also more wordily called the time-corrected

28 Acoustics Today, July 2006

“One especially useful

improvement on the

spectrogram was devised

and implemented as s

oftware thirty years ago,

but it was somehow

drowned in the signal

processing hubbub.”

instantaneous frequency) spectrogram by

a small number of applied researchers.

To understand the new approach,

one must consider the signal as a superposition,

not of pure sine waves as

Fourier taught us, but rather of the generalized

line components already mentioned,

which may have amplitude or frequency

modulation. The objective now is

to compute the instantaneous frequencies

of these line components as the signal

progresses through time. Because of a

duality within the procedure, it is also

possible to compute a sort of “instantaneous

time point” for the excitation of

each line component along the way,

which is technically the group delay associated

with each digital time index.

Note that since there is no mathematically unique

way to decompose a signal into line components, the

decomposition always depends upon the analysis frame

length, with longer frames able to capture lower-frequency

components and also to resolve multiple components

which are close in frequency. Yet, each different decomposition

of a signal is an equally valid representation of its

physical nature—it is up to the analyst to decide whether a

long or short frame analysis is appropriate to highlight the

physical aspects that are of interest in a particular case.

As Kodera et al. demonstrated, the partial derivative in

time of the complex short-time Fourier transform (STFT)

argument defines the channelized instantaneous frequencies,

so that in the digital domain each quantized frequency bin

is assumed to contain, at most, one line component, and the

instantaneous frequency of that component is thus computed

as the time derivative of the complex angle in that frequency

bin. 10 Dually, the partial derivative in frequency of

the STFT phase defines the local group delay, which provides

a time correction that pinpoints the precise occurrence

time of the excitation of each of the line components.

10 In a reassigned spectrogram (e.g., Figs. 2 and 4) the

computed line components are plotted on the time-frequency

axes, with the magnitude of the STFT providing the

third dimension just as in the conventional spectrogram.

One literally reassigns the time-frequency location of each

point in the spectrogram to a new location given by the

channelized instantaneous frequency and local group delay,

whereas in the conventional spectrogram the points are

plotted on a simple grid, at the locations of the Fourier frequencies

and the time indices. A by product of this is that

the reassigned spectrogram is no longer a time-frequency

representation, nor even the graph of a function; the images

presented here are 3D scatterplots with their z-axis values

shown by a colormap. This article will not delve into the

particular algorithms that may be used to compute a reassigned

spectrogramthe problem there is in essence how

one computes the time and frequency derivatives of the complex

STFT argument. An historical and technical review of

the subject, complete with a variety of algorithms for computation,

is provided elsewhere by the authors. 13

Applications of the reassigned spectrogram

The above explanations show that a goodly amount of

reconceptualizing and unfamiliar new mathematical values

are involved in the reassigned spectrogram, and applied

researchers are going to want a big payoff in order to find all

this worth while. Are we seriously going to toss aside the

principles of Fourier analysis in favor of something new? The

proof of the pudding is in the eating, so the chief justification

for doing so is that we will then be better able to see and

measure quantities of interest.

Speech sound analysis

One of the most important application areas of this technology

is the imaging and measurement of speech sound. It has

been found to be particularly useful for analyzing the fine scale

time-frequency features of individual pulsations of the vocal

cords during phonation. The phonation process involves the

repetitive acoustic excitation of the vocal tract air chambers by

the periodic release of air puffs by the vocal cords, which in an

idealized model provide spectrally tilted impulses. As Fig. 4

shows, the reassigned spectrogram provides an impressive picture

of the resonance frequencies (known as formants) and their

amplitudes following excitation by each such impulse.

The speech signal in Fig. 4 was produced using creaky

phonation, which has a very low frequency and airflow, and is

thus quite pulsatile. This is to eliminate aeroacoustic effects and

render the process as purely acoustic as possible for illustration.

Under more natural phonatory conditions, the process is

significantly aeroacoustic, meaning that the higher airflow of

ordinary speech cannot be neglected and has clearly observable

effects on the excitation of resonances. The complexity

of real phonation often militates against the measurement of

formants, but we hope that the reassigned spectrogram can

make such measurement possible, even easy.

Fishy signals

Gymnotiform fish of the tropical Americas and Africa produce

quasi-sinusoidal electrical discharges of low amplitude by

means of a neurogenic organ. 14 While not acoustic in nature, the

signals are now believed to have a communicative function, and

so the effective analysis of such signals poses a problem that is

very much in the vein of bioacoustic signal processing.

Fig. 4. Conventional and reassigned spectrograms of several vocal cord pulsations

during the vowel [e] ‘hay’ pronounced with creaky phonation; computed using 7.8

ms analysis frames. Vocal tract resonances appear as red or yellow excitations at

each impulse, and they decay for some time before the next impulse.

Fig. 5. Conventional and reassigned spectrograms of the same vowel as in Fig. 4,

this time pronounced normally within an English word; computed using 5.9 ms

frames. Note how the pattern of vocal tract excitations has changed from Fig. 4,

although the same vowel is pronounced by the same speaker. Differences are largely

due to the different voice quality of normal phonation.

A Spectrogram for the Twenty-First Century 29

A signal resulting from a pair of brown ghost fish

(Apteronotus leptorhynchus) interacting can display at least

two such components, and the fish have been described as

abruptly moving the frequencies of their signals quite considerably

in response to one another. Recent analysis performed

by the first author in collaboration with John Lewis

and Ginette Hupe of the University of Ottawa, however,

reveals that these interactive modulations may instead

involve only a slight adjustment of signal frequencies to

induce different beat frequencies in the resulting combination

tone. The auditory impression of a brief change in beating

is often that of a chirp or abrupt change in fundamental

frequency. Without the precision of the reassigned spectrogram,

the resolution and measurement of closely aligned and

beating gymnotid signals has been a serious challenge in the

past. Figure 6 shows both a long and a short frame analysis of

the same brown ghost signals; the long frame resolves the

closely spaced line components, but does not have sufficient

time resolution to show the beating between them, while the

short frame fails to resolve the multiple components, but

gains the ability to show the individual beats as impulse-like

signal elements.

Fig. 6. Brown ghost fish signals interacting; upper panel analyzed with 200 ms

frames, lower panel with 10 ms frames. The long frame reveals the small changes

in fundamental frequencies of closely spaced components, while the short frame is

unable to resolve the multiple components but shows the beats as quasi-impulsive

amplitude modulations.

Sound modeling

Additive sound models represent sounds as a collection

of amplitude- and frequency-modulated sinusoids. The timevarying

frequencies and amplitudes are estimated from peaks

in the spectrogram. These models have the very desirable

property of easy and intuitive manipulability. Their parameters

are easy to understand and deformations of the model

data yield predictable results. Unfortunately, for many kinds

of sounds, it is extremely difficult, using conventional techniques,

to obtain a robust sinusoidal model that preserves all

relevant characteristics of the original sound without introducing


For example, an acoustic bass pluck is difficult to model

because it requires very high temporal resolution to represent

the abrupt attack without smearing. In fact, in order to capture

the transient behavior of the pluck using a conventional

spectrogram, a window much shorter than a single period of

the waveform (which is approximately 13.6 ms in the example

shown in Fig. 7) is needed. Any window that achieves the

desired temporal resolution in a conventional approach will

fail to resolve the harmonic components.

An additive model constructed by following ridges on a

reassigned spectrogram yields greater precision in time and

frequency than is possible using conventional additive techniques.

15 From the reassigned spectral data shown in Fig. 7,

we can construct a robust model of the bass pluck that captures

both the harmonic components in the decay and the

transient behavior of the abrupt attack. Sounds reconstructed

from a reassigned additive model preserve the temporal

envelope of the original signal. Time-warping, pitch shifting,

and sound morphing operations can all be performed on the

model data while retaining the character of the original


It is useful to emphasize that the single attack transient in

the bass pluck has been located in time to a high level of precision

using long analysis windows which resolve the harmonics,

a feat that is not possible with the conventional spectrogram.

This is not to suggest that two closely spaced transients

could be resolved if they both fell within a single analysis


Improving on the improved

In spite of the obvious gains in clarity of the locations

and movements of line components in these reassigned spectrograms,

as well as the improved time localization of impulsive

events, the images can be cluttered with meaningless

random points. This is mainly because the algorithm

employed to locate the AM/FM components in the signal has

a meaningful output only in the neighborhood of a component.

Where there is no component of significant amplitude,

the time-frequency locations of the points to be plotted can

become random.

We next describe a technique theoretically outlined by

Doug Nelson of the National Security Administration at Fort

Meade, which has the potential to “denoise” our spectrograms,

and also to permit quasistationary (low FM rate)

components to be isolated in a display, or alternatively to permit

highly time-localized points (impulses) to be isolated.

30 Acoustics Today, July 2006

Fig. 8. Here the reassigned spectrogram of Fig. 4 has been plotted to show only those

points which are part of a nearly stationary line component, found using Nelson’s

higher-order partial derivative condition. These points have a frequency derivative

of the instantaneous frequency within 0.25 of 0.

vocal tract resonance frequencies are much easier to measure

in the lower panel, where they are isolated, than in the upper


Fig. 7. Reassigned spectrograms of 70 Hz acoustic bass pluck, computed using a

Kaiser window of 1901 samples at 44.1 kHz. Both the transient attack and the harmonics

are able to be captured with one choice of analysis frame. Lower panel

shows a different view of the same 3D scatterplot, making it clear how the ridges

could be tracked for additive sound modeling.

Nelson 16 explained that the nearly stationary AM/FM components

of a signal have a frequency derivative of the instantaneous

frequency near zero. By plotting just those points in

a reassigned spectrogram meeting this condition on the

higher-order mixed partial STFT phase derivative to within a

threshold, a spectrogram showing just the line components

can be drawn (Fig. 8). The precise threshold can be empirically

determined, and will in practice depend on the degree

of deviation from a pure sinusoid that is tolerable in the

application at hand.

Nelson further asserted the dual fact that the impulses in

a signal have a value for this same mixed partial phase derivative

near 1. By plotting just those points meeting this condition

to within a threshold, a spectrogram showing just the

impulsive events in a signal can alternatively be drawn (Fig.

9). Plotting all points meeting the disjunction of the above

conditions results in a denoised spectrogram showing quasisinusoidal

components and impulses together, to the exclusion

of most everything else. Figure 10 shows another

demonstration of the usefulness of Nelson’s idea; the excited


The reassigned spectrogram is a technique for analyzing

sound and other signals into their AM/FM components, and

showing the time course of the amplitudes and instantaneous

frequencies of these components in a 3D plot. While similar

in spirit to the 60-year old spectrogram which it improves

upon, it embodies a fundamental departure from the timeworn

efforts to show the complete energy distribution of a

signal in time and frequency. In working to perfect the

method as well as our understanding of the resulting images,

the researchers who have contributed to this technology over

the past 30 years—sometimes in ignorance of each other’s

Fig. 9. Here the reassigned spectrogram of Fig. 4 has been plotted to show only those

points which are part of an impulse, found using Nelson’s higher-order partial

derivative condition. These points have a value for the derivative within 0.25 of 1.

A Spectrogram for the Twenty-First Century 31

1 W. Koenig, H. K. Dunn, and L. Y. Lacy, “The sound spectrograph,”

J. Acoust. Soc. Am. 18(1), 19-49 (1946).

2 G. A. Kopp and H. C. Green, “Basic phonetic principles of visible

speech,” J. Acoust. Soc. Am. 18(1), 74-89 (1946).

3 L. K. Montgomery and I. S. Reed, “A generalization of the

Gabor-Helstrom transform,” IEEE Trans. Information Theory

IT-13, 344-345 (1967).

4 D. Gabor, “Theory of Communication,” J. Inst. Elect. Eng. Part

III 93(26), 429-457 (1946).

5 J. R. Carson, “Notes of the theory of modulation,” Proc. Inst.

Radio Eng. 10(1), 57-64 (1922).

6 J. R. Carson and T. C. Fry, “Variable frequency electric circuit

theory with application to the theory of frequency-modulation,”

Bell Syst. Tech. J. 16(4), 513-540 (1937).

7 K. Kodera, C. de Villedary, and R. Gendrin, “A new method for

the numerical analysis of non-stationary signals,” Phys. Earth

and Planetary Interiors 12, 142-150 (1976).

8 K. Kodera, R. Gendrin, and C. de Villedary, “Analysis of timevarying

signals with small BT values,” IEEE Trans. Acoust.,

Speech, and Sig. Proc. ASSP-26(1), 64-76 (1978).

9 A. W. Rihaczek, “Signal energy distribution in time and frequency,”

IEEE Trans. Information Theory IT-14(3), 369-374 (1968).

10 D. J. Nelson, “Cross-spectral methods for processing speech,” J.

Acoust. Soc. Am. 110(5), 2575-2592 (2001).

Fig. 10. A few milliseconds from vowel [ae] “had,” comparing the visibility of resonance

components in a conventional spectrogram (upper) against a reassigned

spectrogram plotted using Nelson’s component isolation technique. Both are computed

using 5.9 ms analysis frames.

work—have each recognized that, for many applications, it is

the components of a signal that contain the most sought

information, not the overall energy distribution. Going hand

in hand with this break from tradition, by focusing entirely

on instantaneous frequencies the method sets aside the “classical”

Fourier spectrum which decomposes a signal (or its

successive frames, in the spectrogram) into sine waves of

infinite extent. From the perspective of signal modeling, we

already know that real signals are never so constituted, so it

is not exactly a leap of faith to stop representing them that

way. It is our hope that the future will bring production-quality

software that everyone can access, which allows a choice

between conventional and reassigned spectrograms. For

many applied acousticians, the choice will be clear.AT

11 T. Nakatani and T. Irino, “Robust and accurate fundamental frequency

estimation based on dominant harmonic components,” J.

Acoust. Soc. Am. 116(6), 3690-3700 (2004).

12 F. Auger and P. Flandrin, “Improving the readability of time-frequency

and time-scale representations by the reassignment

method,” IEEE Trans. Sig. Proc. 43(5), 1068-1089 (1995).

13 S. A. Fulop and K. Fitz, “Algorithms for computing the time-corrected

instantaneous frequency (reassigned) spectrogram, with

applications,” J. Acoust. Soc. Am. 119(1), 360-371 (2006).

14 J. L. Larimer and J. A. MacDonald, “Sensory feedback from electroreceptors

to electromotor pacemaker centers in gymnotids,”

Am. J. Physiol. 214(6), 1253-1261 (1968).

15 K. Fitz and L. Haken, “On the use of time-frequency reassignment

in additive sound modeling,” J. Audio Eng. Soc. 50(11),

879-893 (2002).

16 D. J. Nelson, “Instantaneous higher order phase derivatives,”

Digital Sig. Proc. 12, 416-428 (2002).

References for further reading:

32 Acoustics Today, July 2006

Sean A. Fulop received a

B.Sc. in Physics (1991) from the

University of Calgary and, after

two M.A. degrees in Linguistics,

received his Ph.D. in Linguistics

(1999) from the University of

California, Los Angeles. He then

held temporary faculty positions

in Linguistics at San José State

University and the University of

Chicago before joining the faculty

at California State

University, Fresno, as an Assistant Professor of Linguistics in

2005. His publication areas range widely in linguistics and

speech and cover speech processing, phonetics, mathematical

linguistic theory, and computational linguistics. His chief

research programs in acoustics involve the investigation of

speech sounds, and the development, evaluation, and dissemination

of improved signal processing tools for phonetics and

speech acoustics research. He currently reviews speech-related

patents for the Journal of the Acoustical Society of America, and

has been a member of the Society since 1987.

Kelly Fitz received a Ph.D.

in Electrical Engineering from

the University of Illinois at

Urbana-Champaign in 1999.

He was the principal developer

of the sound analysis and synthesis

software Lemur and at

the National Center for

Supercomputing Applications.

He was co-developer of the

Vanilla Sound Server, an application

providing real-time

sound synthesis for virtual environments. Dr. Fitz is currently

Assistant Professor of Electrical Engineering and

Computer Science at Washington State University, and the

principal developer of the Loris software for sound modeling

and morphing. His research interests include speech

and audio processing, digital sound synthesis, and computer

music composition.

A Spectrogram for the Twenty-First Century 33

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